Sentence examples for mixed type equation from inspiring English sources

The proof is based on the short time existence of C2,¯γs-smooth solution, the global C1s-estimate, the Hölder estimate of divergence type degenerate equation with measurable coefficients and C1,¯γs-estimate of mixed type equation with Lipschitz coefficients.

In most of the works devoted to the study of mixed type equations, the object of study was mixed elliptic-hyperbolic type equations.

The theory of mixed type equations is one of the principal parts of the general theory of partial differential equations.

Furthermore, as applications, coercivity estimates in Hölder norms for approximate solutions of the multipoint nonlocal boundary value problems for mixed type equations are obtained.

The first fundamental research on the theory of mixed type equations are the works of F Tricomi, S Gellerstedt, which were published in the 1920s.

The actuality of the consideration of mixed type equations has been mentioned, for the first time, by S. A. Chaplygin in 1902 in his famous work 'On gas streams' [1].

It should be noted that problems for a class of fractional differential system and for the non-line differential equations with integral conditions were investigated in [26 30] and BVPs for the mixed type equations involving the Caputo and the Riemann-Liouville fractional differential operators were investigated by many authors; see for instance [31 33].

Consider the jump problem and problems with defects on the type change line for the mixed-type equation of the first kind (1.1).

This equation is a model equation among mixed-type equations of the first kind.

The jump problem and problems with defects on the type change line for model mixed-type equations in the mixed domains are investigated.

For different statements of multidimensional Darboux-type problems or some related Protter-Morawetz problems for mixed-type equations, see [1, 6 13].